Question: Solve for $y$, $ -\dfrac{8}{y + 5} = -\dfrac{1}{y + 5} - \dfrac{4y + 9}{3y + 15} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $y + 5$ $y + 5$ and $3y + 15$ The common denominator is $3y + 15$ To get $3y + 15$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ -\dfrac{8}{y + 5} \times \dfrac{3}{3} = -\dfrac{24}{3y + 15} $ To get $3y + 15$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{1}{y + 5} \times \dfrac{3}{3} = -\dfrac{3}{3y + 15} $ The denominator of the third term is already $3y + 15$ , so we don't need to change it. This give us: $ -\dfrac{24}{3y + 15} = -\dfrac{3}{3y + 15} - \dfrac{4y + 9}{3y + 15} $ If we multiply both sides of the equation by $3y + 15$ , we get: $ -24 = -3 - 4y - 9$ $ -24 = -4y - 12$ $ -12 = -4y $ $ y = 3$